Question

A concave mirror of focal length \( f \) in air is dipped in a liquid of refractive index \( \mu \). Its focal length in the liquid will be:

• A. \( \frac{f}{\mu} \)
• B. \( \frac{f}{(\mu - 1)} \)
• C. \( \mu f \)
• D. \( f \)

Hint:

The focal length of a mirror is not affected by the refractive index of the medium, unlike lenses where the focal length changes with the refractive index of the medium.

Answer 1

The Correct Option is D

This inquiry concerns the focal length of a concave mirror submerged in a liquid with a refractive index of \( \mu \). The critical distinction lies in how a mirror's behavior diverges from a lens's when the surrounding medium changes.

Concept:

Mirrors create images through light reflection, not refraction. Consequently, the surrounding medium's properties do not influence a mirror's focal length. Unlike lenses, whose focal lengths vary with the surrounding medium, a mirror's focal length is invariant.

Explanation:

1. A spherical mirror's focal length is dictated solely by its physical form, specifically its radius of curvature, as defined by the formula:

\(f = \frac{R}{2}\)

1. In this equation, \( R \) represents the mirror's radius of curvature. The absence of the refractive index \( \mu \) from this formula confirms that it has no bearing on the mirror's focal length.

Conclusion:

1. Therefore, the focal length of a concave mirror persists unchanged when it is situated in a medium with a different refractive index.
2. The focal length is \( f \).

The correct option is:

\( f \)